scholarly journals Determinantal Representations of the Core Inverse and Its Generalizations with Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ivan I. Kyrchei

In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derived by using determinantal representations of the Moore-Penrose and Drazin inverses previously obtained by the author. Since the Bott-Duffin inverse has close relation with the core inverse, we give its determinantal representation and its application in finding solutions of the constrained linear equations that is an analog of Cramer’s rule. A numerical example to illustrate the main result is given.

2019 ◽  
Vol 42 ◽  
Author(s):  
Guido Gainotti

Abstract The target article carefully describes the memory system, centered on the temporal lobe that builds specific memory traces. It does not, however, mention the laterality effects that exist within this system. This commentary briefly surveys evidence showing that clear asymmetries exist within the temporal lobe structures subserving the core system and that the right temporal structures mainly underpin face familiarity feelings.


Author(s):  
Yochai Benkler ◽  
Robert Faris ◽  
Hal Roberts

This chapter focuses on the role of the dominant player in conservative media, Fox News, during the first year of Donald Trump’s presidency. It looks at three case studies to illustrate how Fox News used its position at the core of the right-wing media ecosystem repeatedly to mount propaganda attacks in support of Trump: the Michael Flynn firing in March 2017, when Fox adopted the “deep state” framing of the entire controversy; the James Comey firing and Robert Mueller appointment in May 2017; when Fox propagated the Seth Rich murder conspiracy; and in October and November, when the arrests of Paul Manafort and guilty plea of Flynn seemed to mark a new level of threat to the president, Fox reframed the Uranium One story as an attack on the integrity of the FBI and Justice Department officials in charge of the investigation.


2021 ◽  
Vol 11 (1) ◽  
pp. 1-7
Author(s):  
Katharina Pistor

Abstract In this brief introduction, I summarize the core themes of my book “The Code of Capital: How the Law Creates Wealth and Inequality”. Capital, I argue, is coded in law – predominantly in a handful of private law institutions. By relying on legal coding techniques, asset holders invoke the right to enforce claims against others, if necessary with the help of the state’s coercive power.


2020 ◽  
Vol 18 (1) ◽  
pp. 653-661 ◽  
Author(s):  
Hongxing Wang ◽  
Xiaoyan Zhang

Abstract In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse: ||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in {\mathcal R} (M), where M\in {{\mathbb{C}}}_{n}^{\text{CM}} . We get the unique solution to the problem, provide two Cramer’s rules for the unique solution and establish two new expressions for the core inverse.


2021 ◽  
Vol 14 (9) ◽  
pp. e245103
Author(s):  
Rasads Misirovs ◽  
Avinash Kumar Kanodia ◽  
Christopher McDonald ◽  
Richard Green

Mesiodens is the most common type of supernumerary tooth, located between the maxillary central incisors in close relation to the nasopalatine canal. A 20-year-old man presented with right-sided nasal blockage, nasal discharge and collapsed nose without history of trauma. Imaging revealed a calcified mass in the inferior meatus extending into dilated nasopalatine canal. Endoscopic removal of the mass revealed tuberculate appearance of an incompletely developed tooth, consistent with mesiodens. Based on the history of septal cartilage collapse with right-sided mucopurulent discharge, endoscopic findings of the right inferior turbinate being adherent to the septal cartilage and the underlying mesiodens, we believe that the patient developed a septal abscess secondary to infection in nasal mucosa surrounding the mesiodens causing collapse of septal cartilage. While a tooth or tooth-like mass causing nasal passage air-flow obstruction is uncommon, we believe that this is the first reported case of mesiodens presenting with septal cartilage collapse.


2021 ◽  
Vol 138 (1) ◽  
pp. 88-114
Author(s):  
Thino Bekker

The summary judgment procedure in South African law provides for a speedy judgment in favour of a deserving plaintiff where it can be shown that the defendant does not have a triable defence. In 2019 the Rules Board made certain drastic amendments to the procedure of summary judgment in the high court. In this article the historical development of the procedure of summary judgment will be discussed, and the new amendments to rule 32 of the Uniform Rules of Court critically evaluated. It will be argued that the amendments to rule 32 were unnecessary and that it may diminish the right to access to justice in civil disputes. It will, however, also be argued that there are some merits in the critique raised by the Rules Board in relation to rule 32 and that the Rules Board missed a golden opportunity to overhaul the entire summary judgment procedure in a more sensible manner and in line with the core constitutional values of s 34 of the Constitution. It will be argued that rule 32 should be replaced in its entirety by a new, more streamlined procedure, and some recommendations for legal reform will be made in this regard.


Author(s):  
J. T. Cunningham

On May 4th of the current year a number of small Pleuronectids were captured by the hand in a pool left by the ebb tide at Plymouth Breakwater, and brought to me alive. Two of them were very transparent, and, from their habit of lying on the right side when at rest, evidently sinistral forms. One of them was almost perfectly symmetrical; while in the other the torsion of the facial region and eyes had commenced. The pigmentation had the form of interrupted transverse bands, which were most conspicuous on the dorsal and ventral fins; on the dorsal fin seven bands were indicated. The terminal portion of the original trunk, containing the notochord, was seen at the upper edge of the caudal fin. The neurochord was covered with pigment, forming a very distinct band, situated, however, not in the skin, but in the connective tissue surrounding the neurochord or spinal cord. The mouth was large, and the snout upturned. The pectoral fin was large, the pelvic small. But the most important characteristic was the presence of two straight spines projecting laterally from the auditory region. These have been called otocystic spines by Prof. McIntosh, but I think they would be more appropriately described as periotic spines, as they are evidently projections of the periotic cartilage or bone; to which particular bones of the periotic region they belong has not been determined. Mr. Holt cut sections of the spines in situ, and found that they consisted of a knob of periotic cartilage passing into a mass of undifferentiated cells, the whole forming the core of a dermal spine consisting of hyaline ossified tissue. In my specimens I observed a third spine, much smaller, situated in the region of the frontal bone, behind and above the eye; it was visible in both the stages.


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